The most common and most likely answer to this crossword clue is the 7 letter word PROMOTE
I've seen this crossword clue in The Times
P
R
O
M
O
T
E
Buddy explains!

The straight part
We know that "put forward" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case put forward = promote.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does PROMOTE mean?
PROMOTE verb- To raise (someone) to a more important, responsible, or remunerative job or rank.
- To advocate or urge on behalf of (something or someone); to attempt to popularize or sell by means of advertising or publicity.
- To encourage, urge or incite.
- (usually in passive form) To elevate to a higher league.
- To increase the activity of (a catalyst) by changing its surface structure.
- To exchange (a pawn) for a queen or other piece when it reaches the eighth rank.
- To move on to a subsequent stage of education.