Fuji, this is not as straight forward as it might seem. An Approach Control service can provide many elements of that service. The easy ones are the alerting service and flight information service. In practice this is the basic level of service that many approach control units will provide to a VFR flight.
If you're IFR it gets a bit more complicated and depends whether you're inside controlled airspace (CAS) or not and whether the service is provided with or without radar.
I'll deal with the non-radar service first because it sounds like that's what you're talking about. Inside CAS you will be provided with standard separation from other IFR flights that are also inside the controlled airspace. Outside CAS you'll be provided with standard separation from other participating IFR traffic, that is to say, from other IFR aircraft that have asked for a service from the Approach Control Unit and which ATC have agreed to give a service to. This last bit is important because providing a service outside CAS is subject to workload and if you're known to be a training flight they may choose not to provide a service. It's not ideal but in these circumstances airmanship becomes important to ensure that you stay away from the aerodrome by a safe, but undefined, distance. The only thing that I can think of that's laid down is that you cannot enter the aerodrome traffic zone.
If the ATC service is being provided with the aid of radar and outside CAS you have the option of asking for a Radar Advisory Service. This gets to be a very grey area and I don't think that there are easy generic answers.
The standard rules that controllers apply are in the
Manual of Air Traffic Services Part 1 Section 1 Chapter 5 which may be of interest.