How/When to Negotiate Pay?

Hi everyone,

I just received an offer to join as a specialist tutor and am thrilled! However, given my previous experience (top tier work experience within my field + previous experience working at a competitor where I was paid a higher rate), I believe I can ask for a bit more. How/when should I do this? Is this something I do before submitting the new hire form? Do I just reply to their email with my counter? Thank you!