I think you would use something like thenhttps://docs.rs/combine/4.6.3/combine/trait.Parser.html#method.then .

header()
   .then(|header| {
        parse(|input| {
             // Do a separate parse at the offset(s)
             let (output, _input) = my_parser().parse_state(&input[header.offset..])?;
            // Then return the original input to continue parsing there (or return the input where you want to continue parsing)
             Ok((output, input))
        })
   })

That's exact functionality that I need. Thanks!
Let me ask a question, what do you think about new in-crate parser called offset. It's kind of look_ahead + skip: we go to our offset as the current base index, but when we're out of this parser it uses previous index. I can provide test implementation of my idea, just let me know what you think about it.

Sure, that seems generally useful.