You would like to transfer an outdated iOS app (that needs to be republished) to another developer account. You would like to know if the order of the transfer and the republish matters and if it does, which one should be performed first.
The order of transferring the app and republishing matters. Apple requires publishing one app per developer account. Attempting to republish the app under your partner developer account will lead to either 'This developer team has already been used to submit apps.' error during publishing iOS app or Apple binary rejected due to 4.2.6 and 5.2.1 guidelines, precisely because of the developer account ownership. Therefore, you should first transfer the iOS app, then proceed to republish the app.