A new day infiltrating public mainly for soldier (8)
I believe the answer is:
commando
'for soldier' is the definition.
(I've seen this before)
'a new day infiltrating public mainly' is the wordplay.
'a new day' becomes 'and' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'infiltrating' means one lot of letters goes inside another.
'public' becomes 'common' (similar in meaning).
'mainly' means to remove the last letter.
'common' with its last letter taken away is 'commo'.
'and' put into 'commo' is 'COMMANDO'.
Can you help me to learn more?
(Other definitions for commando that I've seen before include "Army unit" , "A specially trained soldier" , "Kilt-wearer might go" , "Member of a special service military unit" , "Military unit specially trained for raids and assaults" .)