Leave scribbled note offering lift (7)
I believe the answer is:
elevate
'lift' is the definition.
(to elevate is to lift up)
'leave scribbled note' is the wordplay.
'scribbled' indicates an anagram (ie written badly).
'note' becomes 'te' (musical note).
'leave' anagrammed gives 'eleva'.
'eleva'+'te'='ELEVATE'
'offering' acts as a link.
(Other definitions for elevate that I've seen before include "Improve morally" , "Uplift" , "Raise or lift" , "Put on a pedestal" , "Lift - exalt - promote - cheer" .)