Long account by His Excellency (4)
I believe the answer is:
ache
'long' is the definition.
(to long for something is to ache for it)
'account by his excellency' is the wordplay.
'account' becomes 'ac' (abbreviation for account).
'by' means one lot of letters go next to another.
'his excellency' becomes 'he'.
'ac'+'he'='ACHE'
(Other definitions for ache that I've seen before include "Hurt; yearn" , "Similar" , "anguish" , "Play up" , "Feel pain" .)