== This does not read well as a sentence. I understand it, but it could be better.

the second part should be 'please see if it's correct'

the first part 'I have written a sentence using the expression'

--->>>> now I make a sentence, please see it's correct.

so putting it all together.

I have written a sentence using the expression, please see if it's correct.

=== This is a good sentence, you have used 'in our best interest' correctly.

It will be in our best interest if we stop complaining and try to figure out better ways to solve the problem.

thanks, so "in our best interest"means "be good for us“， right?

thank you very much for your kindly help, now I get it.

now I make a sentence, please see it's correct.

It will be in our best interest if we stop complaining and try to figure out better ways to solve the problem.

"It is not for their benefit"

In the example you gave, The client cannot wait any longer as it is not in their benefit to wait for you while other suppliers want to sign in also.
Another example: You have received a far more better job proposition from another company, it will not be in your best interest to stay with the actual employer, it will not be for your benefit to stay in your actual job.

In the context that you gave, it means that there is no benefit for the speaker to

wait any longer before making a decision.

Assuming that the person was speaking to you, they are saying that you might need more time to decide, however other people already have made decisions and waiting

may make them go to another buyer. It implies that there may be a cost to the speaker in a delay.

you could also say 'to our advantage' instead of 'in our best interest'