Court umpires and line umpires are drawn from the same pool of professional officials with, unsurprisingly, the plum job of court umpire going to those who are most highly-ranked by the authorities.
See here:
https://www.theguardian.com/money/2011/jun/18/working-life-tennis-umpire
At a more local level (which, after all, is where all of the top officials have to start) a new recruit has to attend a course and pass an examination to become a line umpire and acquire an LTA Official's licence. Then, with enough experience, they can then take a further course, with a further examination, to become a court umpire. Most officials will only ever work in the field of local club tournaments, etc but the very best will be selected by the LTA to officiate in national and international tournaments. At that stage they might opt to become full-time professional officials, if they think that they can make a living from it.
https://www.lta.org.uk/workforce-venues/officiate-tennis/become-an-official/becoming-an-umpire/