[alkonaut]

I think making small opportunistic fixes is best. Do what you can do without massively delaying your work every time you need to work in that area of the code. That is, leave the code better than you found it, each time.

If you add the new logic this time and also split it into four 500-line methods and maybe a few extra tests, you have done quite a lot and it is likely doable within the time frame of the work you are doing.

But

If there are zero tests and you aren't confident that you can create those tests then I'd bring it up with management. Maybe they'll say that changes in this functionality will be very rare after this small change and that it's very well tested manually and by customers - then that's it. Not all code has to be made concise and elegant, it's better to focus your effort on the code that regularly needs changing. However, in this case I'd ask management to consider not changing it at all, or make sure it will be very well tested manually after your changes).