Peter out to relax after month with runs (8)
I believe the answer is:
decrease
'peter out' is the definition.
(I've seen this before)
'relax after month with runs' is the wordplay.
'relax' becomes 'ease' (I've seen this in another clue).
'after' is a charade indicator (letters next to each other).
'month with' becomes 'dec' (I am not sure about this - if you are sure you should believe this answer much more).
'runs' becomes 'r' (cricket abbreviation).
'dec'+'r'='decr'
'ease' after 'decr' is 'DECREASE'.
'to' is the link.
(Other definitions for decrease that I've seen before include "Make smaller or fewer" , "Abate, diminish" , "Get less" , "Reduction" , "Contract" .)