The Draft mechanism has been around since Classic Traveller, and is an interesting artifact of the rules at this point. Considering that Marc Miller is a Vietnam War veteran, and the generation who wrote the game, the idea of a military draft seem natural to them. The problem, lies in scale and the gradual end of conscription in most countries since the 1970's.
With the changes in military technology in the past decades, a short term draftee is no longer a good idea for a solider, and considering that most Traveller characters are going to be experienced with technology at least as advanced to us as ours is to Stephenson's Rocket, the end of conscription for many forces makes sense, as the sheer complexity of the equipment most troops will be equipped with.
Then I come to scale. The massive Third Imperium has enough sophonts that mass conscription would destroy an enemy under sheer weight of numbers, yet this would be impossible due to bottlenecks in interstellar transport. Ships that can carry people are reasonably common IMTU, as anyone from most worlds should have seen one, but the idea of moving a million-man ground force is impractical. The requirements to man most military forces could easily be met by volunteers. As an example, the 1980's US military had over 2,000,000 all volunteer personnel out of a population of 224,000,000. The Imperial forces should be easily manned from volunteers in any case.
That leaves us with the 'Draft' mechanic then, and how to square the circle, metaphorically speaking, of a draft yet having an all volunteer force. Rather than the Chinese model of there being a draft board with a quota for an area that always meets it quota from volunteers, here's how I think of it.
"The Draft" is formally known as the Imperial Service Lottery in law. Unlike traditional forms of conscription, where young men are pulled into the armed forces, the Imperial Service Lottery works in reverse. Any citizen of the Imperium can apply to the Navy, Marines, Army, Merchant hiring service, Scouts, or an Imperial intelligence service or Law Enforcement agency to join. If the prospective recruit cannot obtain a volunteer slot in a service, during a set period, the prospect is entered in to the Draft. This happens usually on a monthly or quarterly basis. The recruiting managers for the world pull the names entered into the Lottery, and thus receive a partial draft of recruits in this fashion. The service, even if they initially rejected the prospect, must take a draftee. Draftees are required to spend their first term in an enlisted status in the Navy, Marines, and Army. Merchant draftees are assigned to lines with mail contracts, or to a Subsidized Merchant. Scout draftees are infamous for their short careers. Law Enforcement draftees are often assigned to Gendarmes or Starport Security, or other manpower intensive, low skilled tasks. This is, of course, a one-time chance for any applicant.