- I think the word “destination” can be used for “先.”

- I feel that “dispatched worker destination” or “worker placement destination” can express the term depending on the context.

- “Placement” is defined as 職業紹介　(Shogakukan J-E Dictionary)

- The派遣元 in your case is the manpower agency which does the recruiting for other companies.

- The派遣先 is the company to where the recruited personnel are sent to (dispatched) or placed.

http://ja.wikipedia.org/wiki/労働者派遣事業
労働者派遣（ろうどうしゃはけん）とは、雇用形態のひとつ。事業主（派遣元という）[In your particular case, it is the manpower agency.]

労働者派遣の内、派遣先企業での直接雇用を前提とする形態。

文脈により変わってくると思います。

派遣先 company where you are dispatched
派遣先 host company
派遣先 Destination Company
派遣先 transfer locations | host company | Destination Company
派遣先 transfer locations
派遣先会社 companies to which employees are transferred
派遣先会社 destination company
派遣先会社 Destination Company
派遣先到着 arrival at the destination

派遣元責任者 person responsible within the company that supplied the dispatched worker
派遣元責任者 Responsible Person Acting for the Dispatching Undertaking
派遣元管理台帳 Management Record of Dispatching Undertaking
当該派遣元事業主 the operator of the dispatching undertaking concerned
前項の派遣元管理台帳 management record referred to in the preceding paragraph
派遣元事業主」という hereinafter "dispatching operator"
「派遣元の事業」という referred to as "dispatching undertaking"
派遣元事業主に通知する notify the operator of the dispatching undertaking

http://trans.glova.jp/index.php

There were already quite a few suggestions made but I would simply say 派遣元 as a person or company doing the recruiting of personnel and 派遣先 as a person or an entity at the receiving end of the recruiting.