When flying VFR from a Class D airport, there is no need to contact clearance delivery to practice IFR approaches. You may, on the other hand, have to call clearance delivery if that is the local procedure for all departures at that airport. This is not very common at a Class D airport. If a clearance is necessary for VFR flights at a Class D airport, most often it is given through ground control. The US Chart Supplement and/or the ATIS will indicate if it is otherwise.
Normally, a simple indication to ground control of your intentions will suffice. This lets them know how to prepare for your return with the rest of their traffic flow and provide separation. This would be a demonstration of common and professional courtesy. It is not mandatory.
You can request a practice approach once airborne and inbound back to the airport without notifying ATC before your departure. As a matter of fact, it is very common to request a practice approach at any class of airport at a distant destination when making your initial call and position report prior to entering the airspace. Be prepared to be denied the approach if the airport is extremely busy during VMC.