The Four Enemies of the Martyr

Four persons were particularly hated by Becket. Three of them were at some time or other excommunicated by him. All were in the service of Henry II, in his Curia Regis or acted as his personal representatives, as envoys and agents to the Papal Curia or to the courts of Louis VII of France, or the Holy Roman Emperor. After Becket's murder all were well rewarded in later life by Henry II with a bishopric for their services in his cause against Becket and the Church. They were

John of Oxford
Richard of Ilchester
Geoffrey Ridel
Reginald Fitz Jocelin

King Henry's determination to promote them to bishops began after the Coronation of the Young King, the crowning of Henry's eldest son, because it had gone ahead against the pope's strict orders not to do so whilst Becket was in exile. This allowed the Pope to authorise Becket to lay an interdict on Henry's territories as punishment. And the threat and potential consequences of this interdict forced Henry to negotiate seriously with Becket. Henry's plans to reward the four with bishoprics probably along with Becket's excommunications/suspensions of the three (arch)bishops of York, London and Salisbury, his principal episcopal enemies, in 1170 were among the events which precipitated the final crisis that led to Becket's murder.

James J. Spigelman (2004). Becket & Henry: The Becket Lectures. James Spigelman. pp. 231–. ISBN 978-0-646-43477-3.

During Becket's absence in exile five Bishopric's had fallen vacant [ Bath and Wells, Lincoln, ] from which Henry was extracting a huge revenue. The right of electing a bishop or archbishop was, according to ecclesiastical Canon Law, anciently and exclusively in the gift of the priors and chapters of the cathedrals; this practice was confirmed by the royal concessions of kings, by bulls of the several popes, and by custom, Nevertheless the Norman and Plantagenet kings frequently usurped this right, frequently imposing their own candidate on the chapter. It was surely better for Henry to have Becket in England under his direct control rather than causing trouble on the Continent.

Christopher Robert Cheney (1956). From Becket to Langton: English Church Government, 1170-1213. Manchester University Press. pp. 20–.

...

How was the ideal bishop to be found? The Gregorian reformers of the eleventh and twelfth centuries replied: by the process of canonical election by the cathedral chapter - free election - subject always to examination of the elect by higher ecclesiastical authority. Whether free elections were best adapted to produce bishops able to resist the temptations of office and involvement in civil affairs is a nice but hypothetical point. In fact, England under the first Angevin kings seldom saw an election conducted with strict regard for the canons. Normally the king controlled it. It was exceptional for a bishop-elect to get possession of a see in England or Wales if Henry II or Richard or John preferred another candidate. The danger of this, as strict churchmen saw it, was that the king would choose a prelate solely for secular qualities. The suspicion was not wholly justified.

...

Vacant Sees

Technically the See of Canterbury became "vacant" [from the king's point of view] after Becket went into exile late 1164.  It became fully vacant after his murder December 29th 1170.

After Becket fled to France any see or abbacy which fell vacant and required consultation with him to fill it remained vacant. Vacant sees were financially beneficial to the king as he could fill the coffers of his treasury with the revenues deriving from them.

St Asaph became vacant in 1165

Bath (& Wells) became vacant in 1166

Hereford became vacant in 1167

Ely became vacant in 1169

Chichester became vacant in 1169

Winchester became vacant in  1171

Norwich became vacant  in 1174.

King Henry was not in a hurry to have any of these posts filled until he probably realised that if and when Becket returned to England that one of Becket's first acts upon landing back home might be to set in motion elections for that purpose. If they were to be filled Henry wanted men of his own choosing, men who would be favorable and compliant towards his policies.


References

George Lord Lyttelton (1771). The History of the Life of King Henry the Second and of the Age in which He Lived ... 2. Ed. - London, Sandby 1767-1771. Sandby. pp. 3–.

Frank Barlow (1990). Thomas Becket. Chapter 10 - The Road to Glory: University of California Press. pp. 198–. ISBN 978-0-520-07175-9.

Anne Duggan (2004). Thomas Becket. Chapter 8 - A Hollow Peace and After: Bloomsbury USA. pp. ISBN 978-0-340-74137-5.

Everett U. Crosby (2013). The King's Bishops: The Politics of Patronage in England and Normandy, 1066-1216. Palgrave Macmillan. pp. 18–. ISBN 978-1-137-35212-5.

Everett U. Crosby (2013). The King's Bishops: The Politics of Patronage in England and Normandy, 1066-1216. Palgrave Macmillan. pp. 250–. ISBN 978-1-137-35212-5. 

Christopher Harper-Bill; Nicholas Vincent (2007). Henry II: New Interpretations. Boydell Press. pp. 180–. ISBN 978-1-84383-340-6.

Becket controversy - Wikipedia, End of dispute 

Reginald Allen Brown (1983). Anglo-Norman Studies: Proceedings of the Battle Conference 1982. David Walker - Crown and Episcopacy under the Normans and Angevins: Boydell & Brewer. pp. 220–. ISBN 978-0-85115-178-6.

The Court and Household of King Henry II, 1154-1189 
Lally, J. 
Ethesis
University of Liverpool 1970

An Introduction to Punishment, Penance, and Reward: The Case of Thomas Becket - CORE Reader