AてからB as “After A, B”
The AてからB grammar construct is nearly identical to the AてB construction (in the cases in which て indicates a sequential relationship between A and B) and only differs in that it emphasizes this sequential relationship moreso. The て in AてからB indicates that A must be in its て-Form. While similar to the more general AてB construction in that the A and B in this grammar construct can be two separate clauses with two separate subjects, unlike the more general AてB grammar construct, AてからB cannot be used in a sentence more than once (however it can be combined with the usage of AてB in the same sentence).
Shukudai o shite kara terebi o mimashita.
(I watched T.V. after I did my homework.)
(Jouji Washington ga dekakete kara heya o souji shimashita.)
(After Jouji Washington left, I cleaned my room.)
Kesa okite kara ha o migaite ryouri o tsukurimashita.
(After I woke up this morning, I brushed my teeth and made breakfast.)