Wie fragt man in englischen in der Mail, ob es geklappt hat, ob es Neuigkeiten gibt?

Dear...

Following up on our previous correspondence, I'd like to inquire if everything is proceeding according to our agreement.

Do you have any updates?

Please don't hesitate to contact us if you have any further questions or concerns.

Best regards

Dear [insert honorific and name/s],

I would like to circle back to what we have discussed previously on the topic of [insert topic].

Do [you/we/our team] have any update on the matter of XXXXX [optional: since our deadline is fast approaching; insert deadline]?

Thank you for [your help/patience/...]

Regards,
[your honorific and name, job title and possibly company, depending on whom you´re writing to]