NEW YORK, March 12 (Reuters) - Shares of Arm Holdings , the British chip designer backed by Softbank Group , gained 1.6% to $128.77 on Tuesday as markets braced for increased trading activity following the expiration of the lockup period tied to its blockbuster initial public offering (IPO).

Most market debuts usually include a lockup period of up to six months, in which company insiders and pre-IPO investors are prohibited from selling their shares. This typically limits the amount of shares available for public trading.

With only 9.5% of Arm's outstanding shares available for trading since its September IPO, the expiration on Tuesday of its lockup period is expected to allow more investors to offload a portion of their holdings. Softbank owns a 90% stake or about 930 million shares in Arm. (Reporting by Chibuike Oguh in New York; Editing by Alden Bentley and Jonathan Oatis)