Crossword Genius

It runs into the sea (4)

Ross

I believe the answer is:

pier

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'the sea' is the definition.
Although both the answer and definition are singular nouns, I cannot understand how they can define each other.

'it runs' is the wordplay.
'it' becomes 'pie' (I can't justify this - if you can you should believe this answer much more).
'runs' becomes 'r' (cricket abbreviation).
'pie'+'r'='PIER'

'into' is the link.

Can you help me to learn more?

(Other definitions for pier that I've seen before include "seaside building" , "Supporting structure" , "seaside location" , "sight at the seaside" , "Support member" .)

I've seen this clue in The Globe and Mail.
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