Motorway got on the nerves, so went elsewhere (8)

I believe the answer is:

migrated

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'went elsewhere' is the definition.
The answer and definition can be both to do with motion as well as being past participle verbs.
Maybe they are linked in a way I don't understand?

'motorway got on the nerves' is the wordplay.
'motorway' becomes 'MI' (resembles M1, English motorway).
'got on the nerves' becomes 'grated' (I've seen this in another clue).
'mi'+'grated'='MIGRATED'

'so' acts as a link.

Can you help me to learn more?

I've seen this clue in The Times.

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