When I hear expressions like "you need to get trained up", I think the up is, at best, superfluous and probably grammatically incorrect.
Is that the case, or does the up serve a purpose?
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Up has numerous uses and, as the OED notes, ‘the variety . . . is so great that the adverb comes to present a number of highly divergent and even directly opposite senses’.
Your example is certainly grammatical. The OED’s definition in this sense is
To cultivate or develop (the mind, the spirit, a faculty, etc.), especially for a specified purpose; to accustom to performing a specified function. Also with up.
The use of train up isn’t new. The entry gives this supporting citation from the mid-seventeenth century:
How much more ought a Christian to train up his own heart, and accustome it this way, to be his continual remembrancer of himself.