Character not the first to get urge (4)
I believe the answer is:
itch
'urge' is the definition.
(thesaurus)
'character not the first' is the wordplay.
'character' becomes 'aitch' (aitch is a kind of character).
'not the first' means to remove the first letter.
'aitch' with its initial letter taken away is 'ITCH'.
'to get' is the link.
(Other definitions for itch that I've seen before include "burn" , "Impatient desire (colloq.)" , "Something that needs a scratch" , "Longing; anag. of 19" , "A strong restless desire" .)