A suspended sentence, per se, doesn't prevent you from travelling to, or living in, another country. It's only if, say, there's also a requirement to attend probation appointments that you'd need to be in the UK on the relevant dates.
People on the sex offenders register are required to notify their local police force before travelling to, or moving, abroad. It's not a 'request' to do so; it's simply a 'notification' of your intention to do so. In the vast majority of cases, such travel presents no problems for the offender. However if the police believe that there's a significant risk that the person might commit further offences while abroad, they can apply for a court order to prevent them leaving the country. The offender then has the right to argue against the imposition of such an the order in court, either in person or through legal representation. (I read the details of loads of court cases every day and I can only recall ever seeing just one such court order being applied for by the police and then contested in court. It was when Paul Gadd, a.k.a Gary Glitter, was prevented from moving to Spain through the police obtaining a court order to prevent him travelling there. So such orders seem to be quite rare).
All you do is to notify your local police force of your intention to move abroad and wait to see if they seek a court order to prohibit such a move. If they do make such an application, you'd then need to seek legal advice to help you fight the application.
If you're able to move abroad, you'll still need to return to the UK once per year during the time that you're on the sex offenders register, in order to met the annual notification requirement. (You have to turn up in person at a police station to confirm or update the information on the register).