What happens when a Grand Maester is murdered
This isn't the first time that Grand Maester was executed by the Monarch or ruling authority. King Maegor had three Grand Maesters executed in his brief reign alone. There is list of precedent for that:
- Grand Maester Gawen: Executed by King Maegor, for speaking in favor of ascension of Prince Aegon (Son of Aenys I) to the throne, by beheading.
- Grand Maester Gerardys: Fed by King Aegon II to his royal dragon, Sunfyre.
- Grand Maester Hareth: Executed for treason by an unknown King.
Everytime a Grand Maester was killed, Citadel did send a new one to the King. Citadel does not command any swords or soldiers so they can't possibly defy the royal commands or criticize the actions without fear of meeting the same fate.
The Citadel does object on dismissal of a Grand Maester however, there seem to have been no objections raised after their execution. From ASOS, Tyrion XII:
"Not at all, my lord. Thank the archmaesters of Oldtown, those who
wished to insist on Pycelle's restoration on the grounds that only
the Conclave may make or unmake a Grand Maester."
Bloody fools, thought Tyrion. "I seem to recall that Maegor the
Cruel's headsman unmade three with his axe1."
"Quite true," Varys said. "And the second Aegon fed Grand Maester
Gerardys to his dragon."
Not to mention, these objections were based on legal rights of the conclave, they weren't an act of defiance or criticism of the regime. E.g. That would be like a King taking a stream away from me and me saying "But your Grace, your own Royal father granted that stream to me for perpetuity. That is my right as per the feudal contract". The hostile action would be "Oh may others take you! You blackhearted rogue, you are no King of mine. I will not pay any taxes unless my stream is restored to me". See the difference?
Anyhow every time the execution happened, the Citadel chose a new one and sent him forth which is evident by the fact that Maegor executed three of consecutive grand Maesters which implies that three must have been sent to him as replacement of the previously executed one.
Will Citadel be reluctant?
By precedent, it is unlikely.
However, it is not as simple as historic cases here.
Cersei's rule is currently unrecognized by most powerful lords of seven Kingdoms.
Citadel is located in Old Town, which is under suzreinity of Tyrells of High Garden. Seeing as Tyrells have raised their banners in favor of Daenerys, it is very likely that Citadel may not send a new Grand Maester to Cersei and refuse to recognize her as the Queen given that they are now protected by the might of High Garden, something which wasn't true back in the day of the Dragon Kings.
Remember, one of the titles of Lord Hightower of Oldtown is Defender of the Citadel. Since his overlords, The Tyrells of High Garden are in open rebellion2, it appears to be unlikely that Citadel, emboldened by protection of Hightowers and Tyrells would send a Grand Maester to King's Landing.
A symbol of legitimacy and its impacts on Tyrell goals
Being served by Grand Maester is a sign of legitimacy and providing that to Cersei instead of Daenerys would be detrimental to Tyrell goals here.
From The Princess and the Queen:
Every visible symbol of legitimacy belonged to Aegon. He sat the Iron
Throne. He lived in the Red Keep. He wore the Conquerer’s crown,
wielded the Conquerer’s sword, and had been anointed by a septon of
the Faith before the eyes of tens of thousands. Grand Maester Orwyle
sat in his councils, and the Lord Commander of the Kingsguard had
placed the crown upon his princely head. And he was male, which in the
eyes of many made him the rightful king, his half sister the usurper.
1. Tyrion appears to be wrong in his memories here. At least Gawen was executed by the King himself with Blackfyre, not by his Axeman.
2. As far as Tyrells are concerned, they are in rebellion. They have sent forces to Daenerys. Cersei isn't that much of an idiot to delude herself that Tyrells will accept her rule after her murder of Lord Tyrell and his children. Daenerys isn't going to waste her time in stopping for camps. She has to reach her destination fast and strike hard, due to rules of logistics. Tyrells don't even need to hide their rebellion as Cersei's rule is unrecognized by great lords and there is no danger from the remnants of Lannister army, battered and tired from a long war.