need your input here.
after an excellent completed order from some of my buyers I get requests to connect on maybe linkedin or twitter so as to recommend me to others.
is this right pls, the TOS says we can promote ourselves, is this a safe way to promote my fiverr page without getting banned?
You can promote your gigs on social media, but you cannot give your contact info to buyers. If you somehow find your Fiverr buyers externally (or even if they give you their contact information) you are breaking Fiverr ToS to contact them. If your buyers want to recommend you, there is a social media button available to them when they complete a gig and they are welcome to use it. They can also give their friends your Fiverr contact info, but not your external contact info. Promotion of your gigs is fine, exchanging contact info or contacting your clients is not. If you get caught, you will be banned.