Simultaneously transmitting and reflecting intelligent reflecting surfaces (STAR-IRS) can assist in achieving full-space signal coverage enhancement. Considering eavesdropping channels, a downlink system model with full coverage of STAR-IRS enabled unmanned aerial vehicle (UAV) secure communication is proposed. The aim is to attain the maximal value of the energy efficiency (EE) by exploring the joint resource allocation of the system. To solve this coupling problem, the lower and upper bounds of the sum-rate for legitimate and eavesdropping users are derived respectively, and Lagrange duality theory is employed to deal with the power control problem. Then the reflection/transmission amplitude splitting coefficient optimization of STAR-RIS using the Hybrid whale-bat (HWB) method in energy splitting (ES) mode are considered to fully exploit the performance gains brought by STAR-IRS deployment. Finally, the simulation verifies that the proposed joint design scheme can enormously promote the EE and safety performance of the system.