One's right to be paid, perhaps, without delay (5)
I believe the answer is:
rapid
'without delay' is the definition.
'one's right to be paid perhaps' is the wordplay.
'one's right' becomes 'r' (I can't explain this - if you can you should believe this answer much more).
'to' says to put letters next to each other.
'perhaps' indicates anagramming the letters.
'paid' is an anagram of 'apid'.
'r'+'apid'='RAPID'
Can you help me to learn more?
(Other definitions for rapid that I've seen before include "Electrical connector" , "Happening at great speed" , "Quickly accomplished" , "moving fast" , "Quick or swift" .)