Payment for awful mumps turning up, oddly ugly at first (4,3)
I believe the answer is:
lump sum
'payment' is the definition.
(I have seen 'Single payment' mean 'lump sum' so perhaps 'payment' could also mean 'lump sum')
'awful mumps turning up oddly ugly at first' is the wordplay.
'awful' indicates anagramming the letters.
'turning up' shows that the letters should be reversed in order.
'oddly' means one should take alternating letters (letters in the odd-numbered positions are used).
'at first' says to put letters next to each other.
The alternate letters of 'ugly' are 'ul'.
'ul' backwards is 'lu'.
'mumps' is an anagram of 'mpsum'.
'mpsum' after 'lu' is 'LUMP SUM'.
'for' is the link.
(Other definitions for lump sum that I've seen before include "11 [LOLLY] as single amount" , "Single payment as opposed to a number of smaller ones" , "Substantial payment" , "Single cash payment" , "as pension may be part-paid?" .)