A longing to be head of Harrow, perhaps? (5)
I believe the answer is:
aitch
'be head of harrow perhaps?' is the definition.
I can't judge whether this defines the answer.
'a longing' is the wordplay.
'longing' becomes 'itch' (I've seen this before).
'a'+'itch'='AITCH'
'to' acts as a link.
Can you help me to learn more?
(Other definitions for aitch that I've seen before include "character leading heroes" , "the start of hives?" , "that I will immediately succeed" , "The letter h in full" , "It's dropped by Cockneys" .)