Talk indistinctly on the first of March, say (6)
I believe the answer is:
mutter
'talk indistinctly' is the definition.
(I've seen this before)
'on the first of march say' is the wordplay.
'on' says to put letters next to each other.
'the first of march' becomes 'm' (1st letter of 'march').
'say' becomes 'utter' (to utter something is to speak or say it).
'm' next to 'utter' is 'MUTTER'.
(Other definitions for mutter that I've seen before include "Low continuous sound" , "Talk under one's breath" , "Speak indistinctly or grumble" , "Barely audible utterance" , "German violinist" .)