Hi, Anisek.
I'm not positive about the exact meaning so I think you have to ask the client to be sure.

What I've found though, is that it is also one of the items/divisions/operations for Product Safety (in reducing accidents in factories, etc.)

Please look under 消費者保護への取り組みについて（page 2 of below PDF file）of all the things that are necessary to take care of. 海推 is listed as one of the things for PS (Product Safety) that has to be taken care of, so I suppose that there is a division set up for it, as with the other divisions/operations such as 経理、設計、情シ (which I found to be 情報システム), etc.

http://www.nite.go.jp/jiko/journal/journal_vol7_pdf/journal_...

--- Based on the below PDF file, I am thinking that it could be the abbreviated form for: "海外業務推進部"

1. [PDF]
1 平成 22 年2月 22 日 各 位 会 社 名 株式会社ゼンリン 代表者名 ...
- [ Translate this page ]
File Format: PDF/Adobe Acrobat
2010年2月22日 ... の海外事業展開を推進するための機能として「海外事業本部」を新設します。.... 海外事業本部 海外業務推進部長. ITS事業本部 ITS営業二部 ...
www.zenrin.co.jp/news/pdf/100222.pdf



--------------------------------------------------
Note added at 2 hrs (2010-11-03 12:08:09 GMT)
--------------------------------------------------

Or　海外事業推進 or 海外事業開発推進
Anyway, these are my suggestions! :-)

--------------------------------------------------
Note added at 2 hrs (2010-11-03 12:09:30 GMT)
--------------------------------------------------

In any case, I think they have to do with 海外 and 推進

--------------------------------------------------
Note added at 3 hrs (2010-11-03 13:00:25 GMT)
--------------------------------------------------

My pleasure, Anisek!

--------------------------------------------------
Note added at 5 hrs (2010-11-03 14:31:41 GMT)
--------------------------------------------------

I just realized that it's from Japanese to English so taking a clue from the below, 海推 could be:
-- Overseas Business Development (Department),
-- Overseas Business Promotion (Department)

海外事業 - Suchmaschine von Dokumenten // 09h15.com - [ Translate this page ]
海外事業推進グループ. Overseas Business Development Department. ... 海外戦略本部 海外事業推進部. Overseas Business Promotion Department, Global Strategic ...