Puritan with a shaky grip (4)
I believe the answer is:
prig
'puritan' is the definition.
(thesaurus)
'a shaky grip' is the wordplay.
'a shaky' indicates an anagram.
'grip' is an anagram of 'PRIG'.
'with' acts as a link.
(Other definitions for prig that I've seen before include "Annoyingly arrogant person" , "Sanctimonious person" , "humbug" , "Over-fussy and self-righteous type" , "Stuffed shirt" .)