One in slight trouble, finally gets cover (8)
I believe the answer is:
insulate
'cover' is the definition.
(thesaurus)
'one in slight trouble finally' is the wordplay.
'one' becomes 'a'.
'in' means one lot of letters goes inside another.
'slight' becomes 'insult' (I've seen this before).
'finally' says to take the final letters.
The final letter of 'trouble' is 'e'.
'a' put into 'insult' is 'insulat'.
'insulat'+'e'='INSULATE'
'gets' is the link.
(Other definitions for insulate that I've seen before include "Lean suit (anag.)" , "Protect from heat, cold, noise etc" , "Cover something to prevent loss of heat" , "Cocoon" , "Protect (from, eg, heat)" .)