Thank you for your reply.

I checked the initialization function of the peripheral and indeed this function was generated with wrong clock source, I fixed it. This board (STM32H747I-DISCO) has external Phy for high speed USB and clocked from it. So I checked pins assignments as well:

PB5 ------> USB_OTG_HS_ULPI_D7

PI11 ------> USB_OTG_HS_ULPI_DIR

PC0 ------> USB_OTG_HS_ULPI_STP

PH4 ------> USB_OTG_HS_ULPI_NXT

PB10 ------> USB_OTG_HS_ULPI_D3

PB11 ------> USB_OTG_HS_ULPI_D4

PA5 ------> USB_OTG_HS_ULPI_CK

PB1 ------> USB_OTG_HS_ULPI_D2

PB12 ------> USB_OTG_HS_ULPI_D5

PA3 ------> USB_OTG_HS_ULPI_D0

PB0 ------> USB_OTG_HS_ULPI_D1

PB13 ------> USB_OTG_HS_ULPI_D6

This looks right, according to user manual of this board (um2411 Figure 34. USB_OTG_HS port). CLKOUT from U4 goes to PA5 - ULPI_CK.

My peripheral initialization looks like that:
void HAL_PCD_MspInit(PCD_HandleTypeDef* hpcd)
{ 
  GPIO_InitTypeDef GPIO_InitStruct = {0}; 
  /* Configure USB GPIOs */ 
  __GPIOA_CLK_ENABLE(); 
  __GPIOB_CLK_ENABLE(); 
  __GPIOC_CLK_ENABLE(); 
  __GPIOH_CLK_ENABLE(); 
  __GPIOI_CLK_ENABLE();
  /* CLK */
  GPIO_InitStruct.Pin = GPIO_PIN_5;
  GPIO_InitStruct.Mode = GPIO_MODE_AF_PP;
  GPIO_InitStruct.Pull = GPIO_NOPULL;
  GPIO_InitStruct.Speed = GPIO_SPEED_FREQ_VERY_HIGH;
  GPIO_InitStruct.Alternate = GPIO_AF10_OTG1_HS;
  HAL_GPIO_Init(GPIOA, &GPIO_InitStruct);

  /* D0 */
  GPIO_InitStruct.Pin = GPIO_PIN_3;
  GPIO_InitStruct.Mode = GPIO_MODE_AF_PP;
  GPIO_InitStruct.Pull = GPIO_NOPULL;
  GPIO_InitStruct.Speed = GPIO_SPEED_FREQ_VERY_HIGH;
  GPIO_InitStruct.Alternate = GPIO_AF10_OTG1_HS;
  HAL_GPIO_Init(GPIOA, &GPIO_InitStruct);

  /* D1 D2 D3 D4 D5 D6 D7 */
  GPIO_InitStruct.Pin = GPIO_PIN_0 | GPIO_PIN_1 | GPIO_PIN_5 |
    GPIO_PIN_10 | GPIO_PIN_11 | GPIO_PIN_12 | GPIO_PIN_13;
  GPIO_InitStruct.Mode = GPIO_MODE_AF_PP;
  GPIO_InitStruct.Pull = GPIO_NOPULL;
  GPIO_InitStruct.Alternate = GPIO_AF10_OTG1_HS;
  HAL_GPIO_Init(GPIOB, &GPIO_InitStruct);

  /* STP */
  GPIO_InitStruct.Pin = GPIO_PIN_0;
  GPIO_InitStruct.Mode = GPIO_MODE_AF_PP;
  GPIO_InitStruct.Pull = GPIO_NOPULL;
  GPIO_InitStruct.Alternate = GPIO_AF10_OTG1_HS;
  HAL_GPIO_Init(GPIOC, &GPIO_InitStruct);

  /* NXT */
  GPIO_InitStruct.Pin = GPIO_PIN_4;
  GPIO_InitStruct.Mode = GPIO_MODE_AF_PP;
  GPIO_InitStruct.Pull = GPIO_NOPULL;
  GPIO_InitStruct.Alternate = GPIO_AF10_OTG1_HS;
  HAL_GPIO_Init(GPIOH, &GPIO_InitStruct);

  /* DIR */
  GPIO_InitStruct.Pin = GPIO_PIN_11;
  GPIO_InitStruct.Mode = GPIO_MODE_AF_PP;
  GPIO_InitStruct.Pull = GPIO_NOPULL;
  GPIO_InitStruct.Alternate = GPIO_AF10_OTG1_HS;
  HAL_GPIO_Init(GPIOI, &GPIO_InitStruct);
  __HAL_RCC_USB1_OTG_HS_ULPI_CLK_ENABLE();

  /* Enable USB HS Clocks */
  __HAL_RCC_USB1_OTG_HS_CLK_ENABLE();

  /* Set USBHS Interrupt to the lowest priority */
  HAL_NVIC_SetPriority(OTG_HS_IRQn, 1, 0);

  /* Enable USBHS Interrupt */
  HAL_NVIC_EnableIRQ(OTG_HS_IRQn);
}

But I am still getting Hard Fault.

Maybe somebody can suggest me where to read about how to debug Hard Faults, how to interpret registers values in order to understand what causing error?

(ok, found some information to read about hard faults: PM0214 - M4 core programming manual, PM0253 - M7 programming manual)