After House Helgram, House Jesby is the largest House in the Courts, but tends to have more political power because its members spend much more time working together. Jesby tends to firmly adhere to the status quo, whatever it may be; this does not make it a particularly exciting or interesting House, but its reputation for reliability and loyalty makes it strong and favoured by the king.
"It was Tmer of House Jesby, eldest son of thee late Prince Rolovians, and now lord himself of the Ways of Jesby--spade beard, heavy brow, sturdily built, not unhandsome in a rugged sort of way; by all report, a brave and possibly even sensitive fellow..." --Merlin, Prince of Chaos
Tmer is the current head of Jesby. The killings that went on two decades back during Swayvill's brush with death have left him one of Swayvill's closest relatives; by some interpretations, he would inherit the throne if Swayvill were to die tomorrow.
This has made Tmer, a man more noted for his love of rare books than for his political skill, both an extremely cautious man and extremely nervous one. He tends to keep to his House and avoid saying anything that might be construed as showing any desire for the throne. House Jesby's fortunes have suffered somewhat because of this, and there are whispers both within and without the House that Tmer will soon step down (or be forcibly removed) as the head of Jesby.