One succeeding that's to come up in an hour (4)
I believe the answer is:
heir
'one succeeding' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'that's to come up in an hour' is the wordplay.
'that's' becomes 'ie'.
'to come up' shows that the letters should be reversed in order.
'in' is an insertion indicator.
'an hour' becomes 'hr' (abbreviation).
'ie' written backwards gives 'ei'.
'ei' going within 'hr' is 'HEIR'.
Can you help me to learn more?
(Other definitions for heir that I've seen before include "Acknowledged beneficiary" , "One likely to succeed" , "One who will succeed to title" , "Legal successor" , "One due to inherit" .)