combine two GCC compiled .o object files into a third .o file

Passing -relocatable or -r to ld will create an object that is suitable as input of ld.

$ ld -relocatable a.o b.o -o c.o
$ gcc c.o other.o -o executable
$ ./executable

The generated file is of the same type as the original .o files.

$ file a.o
a.o: ELF 32-bit LSB relocatable, Intel 80386, version 1 (SYSV), not stripped
$ file c.o
c.o: ELF 32-bit LSB relocatable, Intel 80386, version 1 (SYSV), not stripped

If you want to create an archive of two or more .o files (i.e.. a static library) use the ar command:

ar rvs mylib.a file1.o file2.o