I am using post request to retrieve route between two locations. (https://api.openrouteservice.org/v2/directions/driving-car). Is it possible to retrieve map image during this request. Or I have to request another api?
no, the openrouteservice is only concerned with routing, not with the underlying map images.
Have a look at the OSM wiki - you’ll find information about raster tiles, vector tiles and servers for different styles.