The 'Fardh' (obligatory) prayers have priority over any other 'ibada' and or 'nafil' prayers.
If the 'iqama' of any 'fardh' prayers is started then one should shorten his 'nafil' prayers and join the 'fardh' prayers.
However, one humble suggestion in this regard that one should see whether any convenient time is left for any 'nafil' prayers, then he should go for that prayers.
P.S: I am not a mufti or scholar of religion but simply a student of religion. This is my logical opinion, some may differ with it.
Allah knows the best.