To resolve a problem promptly means to take action to solve the problem as soon as possible. Here are some ways you can say this in Engpsh:

"Let's take care of this issue right away."
"We need to address this problem as soon as possible."
"We should try to resolve this issue as quickly as we can."
"It's important that we deal with this problem promptly."

If you want to be more formal, you could say:

"It is imperative that we address this issue in a timely manner."
"It is of the utmost importance that we resolve this problem as promptly as possible."