No, there's implied clearance to enter class d CTR, by the tower simply acknowledging you.
ESTABLISHING TWO-WAY COMMUNICATIONS
When an aircraft contacts ATC at a class D aerodrome and provides sufficient information about track, position, level, and intentions, ATC may give a clearance to enter the airspace by simply acknowledging the transmission with the aircraft’s callsign. Alternatively, a clearance may be denied, or afforded by an alternate route or level as instructed by ATC. Such instructions may include ‘join crosswind’, ‘overfly’, or ‘report at [position]’. The acknowledgment authorises the aircraft to enter the class D airspace following the stated track and level, or any alternative instruction given by ATC. Pilots are then required to maintain two-way communications with ATC and comply with any subsequent ATC instructions.
This shortened procedure does not eliminate the availability of a ‘traditional’ airways clearance. However, it provides an abbreviated clearance option for use when both pilot and ATC understand the proposed course of action.