Short answer
Usually yes. Independent contractors are not covered by a client's policy and are typically responsible for their own liability, so clients often require them to carry general liability and provide a certificate of insurance. The right coverage depends on the work, and professional services may also need professional liability.
Being an independent contractor means you are your own business, and a client's insurance generally does not extend to you. If your work causes injury or damage, the responsibility is yours, which is why clients frequently require contractors to carry their own general liability and show proof before starting.
The coverage you need follows the work. Trades and physical work lean on general liability, professional and advisory work often needs professional liability, and a contract may specify limits and an additional insured. Carrying your own coverage also makes you easier to hire.
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