Paul’s second long letter (5)
I believe the answer is:
aitch
'letter' is the definition.
(aitch is the name for the letter H)
'paul's second long' is the wordplay.
'paul's second' becomes 'a' (2nd letter of 'paul').
'long' becomes 'itch' (to long or itch for something is to desire it).
'a'+'itch'='AITCH'
(Other definitions for aitch that I've seen before include "Eighth letter of the English alphabet" , "The letter h in full" , "character leading heroes" , "Letter sound that's often dropped?" , "8th letter of the alphabet" .)