Can't power HC-05(5v) with Arduino Pro mini (3.3v)?
It seems like 7.4V DC is greater than the 5V regulator input range on the HC-05.

For example, in the Core Electronics tutorial for the HC-05 (the tutorial PDF calls it a JY-MCU. I can't find any major differences), the pinout table says the voltage should be from 3.6V to 6V DC:



These same values are confirmed by a back-of-the-circuit-board photo from arduino-info.wikispaces:



Components101 says the range is 4V to 6V.

Unfortunately your coin cell voltage is too low. That leaves you with the following options to drop your voltage (if you must use the 7.4V DC battery). Your choice will probably depend on the Wh capacity of your battery, and how efficient you need the voltage drop circuit to be.


Zener diode (few components, inefficient use of power)
Voltage divider with resistors (few components, inefficient use of power)
Linear regulator (few (IC) or many (discrete) components, inefficient use of power)
Switching regulator (many components, efficient use of power (because it does not use a resistor to drop the voltage)


Further details on each of these options are at Lower Voltage Methods Other than Voltage Dividing.