The most common and most likely answer to this crossword clue is the 3 plus 2 letter word EGG ON
I've seen this crossword clue in The Sunday Telegraph
E
G
G
O
N
More clues leading to the result EGG ON
- Foolish person’s face might have this urge
- Urge power company to retain horse
- Incite, say, unlimited agony
- This on top of face is embarrassing? Offer encouragement!
- Horse beset by frantic one with spur
- Encourage, for example, ‘good’ touching
- Toast might have this to encourage
- Prod mine and proceed!
- Incite say Indian to leave area
- Encourage to leave, say, before beginning of November
Buddy explains!
The straight part
We know that "Push" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case push = egg on.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.