Is there any reason not to go up for promotion? I started my first permanent academic position as a Lecturer at at UK university in Autumn 2019. More than one of my senior colleagues seems very eager to get me promoted to a Reader as soon as possible, looking out that I tick the right administrative boxes to make this happen and encouraging me to apply for promotion this month. This seems premature to me as I don't even feel like I know the my way around the university yet, and with Covid I haven't accomplished much in my research since joining the university.
My question is: Are there any reasons not to pursue a promotion? A promotion is a great thing, right? But are there any downsides? E.g. it might make it harder for me to move to a different university in a few years if I want to, or I might get saddled with more administrative responsibilities? Are there any other downsides I haven't thought of?
Not really.  Promotion is primarily about pay (though sometimes the pay increment is small) and recognition of your achievements to those who are not already aware of them.
You are unlikely to get more duties after promotion because you are expected to take on the duties of the higher rank in order to get the promotion.  It's seeking a promotion, not receiving one, that causes you to get more duties.
As you already have a permanent academic position, a change in rank will not make much difference to your mobility; it is already very low.