A rope and lead climbing rack is not essential to climb on trips but you will be more independent and probably find it easier to get climbing partners if you do have some of your own gear.
A trad climbing apprenticeship is generally a good idea before trying to progress through the grades on lead as the consequences of a fall on badly placed gear is serious regardless of how hard the climb is. Specialist trad leading courses are highly recommended to complement your general experience.
A trad lead rack is a huge investment – many climbers go for the cheapest gear to build a rack quickly then end up wanting to replace it as soon as they start progressing through the grades so it’s always worth getting a feel for stuff and trying other peoples before investing. Coordinating gear with someone you climb with a lot is one way to keep the cost down. The Needlesports website has fairly comprehensive trad rack advice, it’s possibly a bit behind the times so below are some further recommendations for certain items based on what is popular in the club. There is loads of other good kit by other brands available beyond what is mentioned below but we are often asked for advice by new climbers and these are all good benchmark recommendations.