The security implications that can occur during exec function call are:-
Providing relative path instead of the absolute path is a major drawback as certain times this path can be altered and can lead to massive errors and this can be avoided by using absolute path.
Since the open file descriptors are shared, this is also a drawback, as there may be certain file descriptors pointing to some sensitive info, to avoid this one should close the important file descriptors before the exec call.
The background processes should also be killed before doing exec.
The environment variables passed during exec system call should also be taken care of, as if not managed properly can wreak havoc, this can be done by only passing those variables which aren't of much use to the system.