add Management vlan in ap and the same vlan in zonedirector, add dhcp to
vlan interface in zonedirector,
the devices that connected to ap can getting ip from mikrotik or zonedirctor or from same ap, and it depend if ap wlan or ether have vlan or no.
if wlan or ether have vlan add same vlan in mikrotik and add dhcp tosame vlan,,,,
if wlan or ether have not vlan untag add dhcp to mikrotik out ether
if you want devices to getting ip from zonedirctor add the same steps in zonedirctor not in mikrotik (vlan tag in ap , vlan tag in mikrotik and vlan tag in zonedirctor dhcp )
if you want devices to getting ip from same ap you can enable local subnet in the ap and enaple it in wlan or ether in ap and devices will getting ip from ap and ap will work as gateway