According to Carrier 4's datasheet it does support a throttle, but has no connection/etc details, so you'll have to ask them which throttle to get for it and where to plug it in, to be certain that this is correct. (I'd also make sure with them which, if any, settings to change in the display setup menus).
CONTROLLER CARRIER 4 51100 DATASHEET BY PROMOVEC JAN. 2018, VS_1 Type Carrier 4
TESTS & SPECIFICATION
Motor code S07
IP IP54
Motor position Front / rear
Certifications CE / EN 15194
SPECIFICATIONS / REACH /ROHS
Voltage 36V
BATTERY INFORMATION
Power rating 250W
Battery type Carrier 4
Light output Yes
Battery communication Yes
Brake cut off support Yes
BB pedal sensor type Speed
OPTIONS Display protocol v1
Wheel size 26” (50974-1-26”)
Speed limit 25 km/t
Walk-assist Yes
DRIVING MODE Speed/ECO
Throttle function Yes
COMPATIBLE MOTORS 50742
WIRING Length:
Connector Battery connection Integrated
COMPATIBLE SENSORS 50960, 50920, 50587
Motor cable Integrated 9 pin circular
BB sensor cable Integrated 5 pin circular
COMPATIBLE DISPLAYS V1
Display cable Integrated V1
Brake cut off + light cable Integrated 3-pin circular
COMPATIBLE BATTERIES Carrier 4: 50640-BL, 50784-BL, 50642-BL 50639-BL