When you say "partner", I assume that you do not have a spouse or you have a civil union which is not recognized by Singapore. If correct, then both of you will require an employment pass to live and work in Singapore. No dependent pass available.
Second, des your partner actually have a job with an International School
lined up? With the school applying for an employment pass? Because right now, and because of Covid, getting new employment passes is very difficult.
Third, it will make no difference to you whether or not your partner has an employment pass. You must get your own employment pass on your own merits.
And that brings us to fourth... that is going to be extremely difficult to do. Maybe your cyber security credentials might get you in, but the fact is, almost nobody applying as a foreigner gets a job in Singapore. Add to that the fact that IT is a sector that the gahmen reserves for local graduates and you are facing a double whammy. Your chances of getting hired are close to zero.
But, find out for yourself. Do a search of MNC's with offices in Singapore. Forget the local firms... you'll never get hired there. For each of the MNC's in Singapore that you select, check out the Singapore jobs. Apply for some of them. See what happens.