The most common and most likely answer to this crossword clue is the 6 letter word ASSURE
I've seen this crossword clue in The Times
A
S
S
U
R
E
More clues leading to the result ASSURE
- Convince Jenny to go by river
- Give guarantee when certain
- Convince son to invest in a safe
- Make certain, as certain can be
- Give confidence when very well
- Guarantee backing for some further US sanctions
- Give confidence when certain
- Give confidence to don, having right to succeed master
- Promise made by fool on northern river
- Tell positively, when certain
Buddy explains!

The straight part
We know that "Convince" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case convince = assure.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 ASSURE mean?
ASSURE verb- To make sure and secure.
- (followed by that or of) To give (someone) confidence in the trustworthiness of (something).
- To guarantee, promise (to do something).
- To reassure.