4-pole jacks have 2 different standards and only one type (OMTP) would work when plugged in to a 3-pole headphone jack.
For proper compatibility either type should be connected via a splitter cable that converts the 4-pole jack connections to a 3-pole speaker jack and 3-pole microphone jack
If the headset jack does not work, it probably has CTIA standard wiring and it needs a splitter with a cross-over connection to work with a headphone jack socket
Headphone Splitter for Computer CTIA 3.5mm TRRS Female to Dual TRS Male Mic Audio Jack Y Adapter Headset Splitter Cable for PC Laptop to Gaming Headset
If the headset is used with other devices, it may be preferable to get a standard splitter cable without the crossover connection and a separate crossover adaptor. 2 adaptors would allow any 4-pole jack to work with any 4-pole or 3-pole jack socket
OP in this topic found a simple way to test an incompatible headset connection: