It is not yet clear how soon Garcia will resign his seat to take the HUD position. Whenever he does, the City Council will declare a vacancy at its next meeting and then a special election to replace him has to take place within 30 to 60 days.
There really is no avoiding a special election on a date of its own since we are still 6 1/2 months from the primary. It will likely be in March or early April.
The politically interesting part of this comes with who is vying to replace him. Paula Sandoval (State Senator: SD34) has already expressed an interest in the seat when it comes open. She would likely resign her senate seat to run (she is term-limited this year anyway). This causes a vacancy committee to replace her.
The SD34 vacancy would likely be filled by either Reps. Jerry Frangas (HD4) or Joel Judd (HD5). This causes even more vacancy committees to replace them.
All of this, of course, is happening when heavily contested primaries were already developing in all 3 of those districts.
And to add insult to injury: The Denver Election Division is scheduled to move their office on March 19th!