DBS (formerly CRB) checks can only be carried out by employers when the job relates to working with children, working with vulnerable adults, working 'in the administration of justice' or certain other specified types of job. They're not available to the majority of employers.
Convictions and cautions are ALWAYS included on DBS checks for such types of employment unless they are 'protected', as below:
A conviction (such as that which resulted in the binding over order) can only become 'protected' if:
(a) it is the person's ONLY criminal conviction ;
(b) it didn't result in a prison sentence (whether or not suspended) ;
(c) it's not a list of excluded offences (such as sexual offences) ; and
(d) ELEVEN YEARS have passed since the date of conviction.
A caution can become 'protected' after SIX YEARS (with there being no limit to the number of cautions which can become 'protected').
So the conviction which led to the binding over order will appear on the person's DBS checks until April 2027 (assuming that the person has never been convicted of another criminal offence and doesn't acquire a further conviction in the future, in which event it would never become 'protected').
The caution will appear on their DBS checks until 6 years have passed since it was given.
For employment applications where DBS checks aren't relevant (i.e. those not exempted from the provisions of the Rehabilitation of Offenders Act 1974, as amended), a binding over order becomes 'spent' (and thus does not need to be declared) as soon as the relevant period ends. A 'simple caution' becomes 'spent' as soon as it's been given, whereas a 'conditional caution' becomes spent after 3 months. (It should be noted though that no conviction or caution can become 'spent' while the person still has another 'unspent' conviction/caution. They will both remain 'unspent' until the later period ends).