How escorts reacted to the loss of HMS Hood

Did ships or intended sister ships ever seek revenge for a vessel that had been sunk?

Yes. Hood's escorts and Tribal-class destroyers were intensely angered by her loss, even though they were not her sister ships.

Hood's escorts and Tribal-class destroyers were intensely angered by her sinking. The bond extended to ships that were not her sisters. Shared service with a lost vessel could give its consorts a strong desire for revenge.