Tramp stumbles across area with last of booze (7)
I believe the answer is:
traipse
'tramp' is the definition.
(thesaurus)
'stumbles across area with last of booze' is the wordplay.
'stumbles' becomes 'trips' ('trip' can be a synonym of 'stumble'**).
'across' indicates putting letters inside.
'area' becomes 'a' (maths abbreviation).
'with' says to put letters next to each other.
'last of' suggests the final letters.
The final letter of 'booze' is 'e'.
'trips' going around 'a' is 'traips'.
'traips'+'e'='TRAIPSE'
(Other definitions for traipse that I've seen before include "Walk heavily" , "Parties (anag.)" , "Tedious walk" , "travel wearily" , "Walk about wearily" .)