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In circumstances where one child has died before their parent, it would be normal for the parent's Will to cater for this situation, in that there would usually be a clause to say that if any child predeceases, his/her share should pass to his/her children.
Not sure if you have children, but you shold first find out what your Father's Will says in respect of the above.
Subject to the above, if you still require a codicil, this of course will need to be signed by your Father in front of 2 independent people (ie witnessed by a party who is not a beneficiary and nor the spouse of any beneficiary can act as witness).
Please note the codicil, once executed, should NOT be stapled to the Will- you should never staple any extra document to a Will, and the codicil should just be placed with the Will.
I hope this assists and answers your question.