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The lawyer made a persuasive statement on his client's behalf.
Literal
Lawyer [topic-は] client [for-のために] persuasive [having-のある] statement [obj-を] made.
~のある ('having X, with X') attaches to a noun + の to form an attributive modifier — 'a Y that has X.' Here 説得力のある発言 = 'a statement having persuasive power.' This ~のある pattern is one of two common attributive options, alongside ~を持つ ('holding X'). 説得力 ('persuasive power, persuasiveness') uses 力 ('power') as a productive abstract-noun suffix: 想像力 (imagination), 判断力 (judgment).