"His European connections are useful."
Translation:Seine europäischen Verbindungen sind praktisch.
The immediate translation of "useful" with respect to connection is "nützlich/wertvoll".
It is possible to invent context in which connection could be called "praktisch" or "sinnvoll", but this is not the immediate translation: "Sinnvoll" would mean "sensible/meaningful" which would be odd words to use about connections. Likewise "praktisch" would mean "practical/handy" in a very concrete way. However connections usually operate less obvious and concrete.
his translates to seine
ihre translates to her, their or your (formal)
'praktisch' and 'nützlich' should be accepted -if you ask me-. 'wertvoll' tells similar facts, but it is too far away from 'useful' in my opinion.
For example: Both microwaves are useful, but you would only need one mircowave. For you one microwave is 'wertvoll' and the other identical microwave you does not need in addition is not 'wertvoll' for you, because you have already one.