Tower where inmate festers, last of four locked up (7)
I believe the answer is:
minaret
'tower' is the definition.
(I know that minaret is a type of tower)
'inmate festers last of four locked up' is the wordplay.
'festers' is an anagram indicator (I've seen 'festering' mean this).
'last of' indicates one should take the final letters.
'locked up' indicates putting letters inside.
The last letter of 'four' is 'r'.
'inmate' anagrammed gives 'minaet'.
'minaet' going around 'r' is 'MINARET'.
'where' is the link.
(Other definitions for minaret that I've seen before include "Slender tower with balconies" , "tower in the Middle East" , "religious tower" , "Mosque's tower" , "Slim tower of a mosque" .)