Letter a problem, the first to be dropped (5)
I believe the answer is:
aitch
'letter' is the definition.
(aitch is the name for the letter H)
'a problem the first to be dropped' is the wordplay.
'problem' becomes 'hitch' (I've seen this before).
'the first to be dropped' means to remove the first letter.
'hitch' with its first letter taken away is 'itch'.
'a'+'itch'='AITCH'
(Other definitions for aitch that I've seen before include "8th letter of the alphabet" , "that may be dropped" , "Eighth letter of the English alphabet" , "what some drop?" , "Letter sound that's often dropped?" .)